2012 # A variational approach to cardiac motion estimation based on covariant derivatives and multi-scale Helmholtz decomposition

**Abstract:** The investigation and quantification of cardiac motion is important for assessment of cardiac abnormalities and treatment effectiveness. Therefore we consider a new method to track cardiac motion from magnetic resonance (MR) tagged images. Tracking is achieved by following the spatial maxima in scale-space of the MR images over time. Reconstruction of the velocity field is then carried out by minimizing an energy functional which is a Sobolev norm expressed in covariant derivatives. These covariant derivatives…

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“…For example, if a = 0 and D would be constant, then by Eq. (20) and Schur's lemma one has D = diag{D 11 , . .…”

confidence: 99%

“…For example, if a = 0 and D would be constant, then by Eq. (20) and Schur's lemma one has D = diag{D 11 , . .…”

confidence: 99%

“…Some of the optic flow methods, such as [55,56,57], do allow direct computation on the original MRI-tagging images as well, but they are relatively expensive, complicated and technical, e.g. [20].…”

confidence: 99%

“…The reader can refer to [16] for a recent review on estimators dedicated to fluid flows and more generally to [1,2,12] for presentation and comparative performance evaluations of some state-of-the-art techniques in computer vision. Interested readers may also refer to [3,7,24], which provide recent trends for data based adaptive deformation estimation schemes.…”

confidence: 99%

“…Several motion estimators dedicated to the measurement of specific phenomenon such as fluid flows have been proposed in the literature (see [16] for a detailed overview). These estimators differ mainly on the smoothness function they are handling: first order penalization [29], second order div-curl regularization [6,33], data-dependent [3,7,24] or power law auto-similarity principles [14,15]. These methods provide accurate instantaneous displacements as they generally implement additional constraints imposed by the physics, as in [6,11] and most of them are embedded into a multiscale formalism that enables capturing efficiently the large scales deformations [16].…”

confidence: 99%